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28 votes
28 votes
How do you know when to factor a negative square root number and when to just find it’s imaginary number

User Hanne
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1 Answer

14 votes
14 votes

sqrt(-44)

This has a perfect square inside the square root

4 is a perfect square

sqrt(-1 * 4 * 11)

sqrt(-1) sqrt(4) sqrt(11)

We know the square root of 4 is 2

2 sqrt(11) sqrt(-1)

2 sqrt(11) i

sqrt(-30)

sqrt( 6*5* -1)

There is no perfect square for 30

Another example with a perfect square inside would be

sqrt(-54)

sqrt( -1 * 27*2)

sqrt( -1 * 9 *6)

9 is a perfect square

sqrt( -1) * sqrt(9) sqrt(6)

3 i sqrt(6)

Try to break down larger numbers and see if there is a perfect square that is a factor

User PEHLAJ
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2.8k points